Mineral resource modelling using an unequal sampling pattern: An improved practice based on factorization techniques

This work addresses the problem of geostatistical simulation of cross-correlated variables by factorization approaches in the case when the sampling pattern is unequal. A solution is presented, based on a Co-Gibbs sampler algorithm, by which the missing values can be imputed. In this algorithm, a heterotopic simple cokriging approach is introduced to take into account the cross-dependency of the undersampled variable with the secondary variable that is more available over the entire region. A real gold deposit is employed to test the algorithm. The imputation results are compared with other Gibbs sampler techniques for which simple cokriging and simple kriging are used. The results show that heterotopic simple cokriging outperforms the other two techniques. The imputed values are then employed for the purpose of resource estimation by using principal component analysis (PCA) as a factorization technique, and the output compared with traditional factorization approaches where the heterotopic part of the data is removed. Comparison of the results of these two techniques shows that the latter leads to substantial losses of important information in the case of an unequal sampling pattern, while the former is capable of reproducing better recovery functions.

Geostatistical modeling of porosity and evaluating the local and global distribution

Porosity is one of the main variables needed for reservoir characterization. For this volumetric variable, there are many methods to simulate the spatial distribution. In this article, porosity was analyzed and modeled in the local and global distribution. For simulation, Sequential Gaussian simulation (SGS) and Gaussian Random Function (GRFS) were applied. Also, kriging was used to estimate the porosity at specific locations. The main purpose of this work was to investigate the porosity to compare geostatistical simulation and estimation methods in a sandstone reservoir as a real case study. First, the data sets were normalized by the Normal Scores Transformation (NST) and stratigraphic coordinate. The model of experimental variograms was fitted in the vertical and horizontal directions. For the simulation methods, 10 realizations were generated by each method. The Q-Q plots were calculated, and both sets of quintiles (Target Porosity Distribution versus Porosity realization) came from normal distributions with the following correlation coefficients: 0.93, 0.94 and 0.97 related to GRFS, SGS and Kriging, respectively. The extracted variograms from realizations showed that the kriging couldn’t reproduce the variograms with global distribution. For local validation, the cross-validation was evaluated and three wells were omitted. The re-estimation of porosity was considered at located well logs through the well sections window where the kriging had a better performance with minimum error to estimate porosity locally. Finally, the cross-sectional models were generated by each algorithm which showed that the simple kriging tries to produce smoother distribution, whereas conditional simulations (SGS and GRFS) try to represent more global-detailed sections.

Regional Geochemical Anomaly Identification Based on Multiple-Point Geostatistical Simulation and Local Singularity Analysis—A Case Study in Mila Mountain Region, Southern Tibet

The smoothing effect of data interpolation could cause useful information loss in geochemical mapping, and the uncertainty assessment of geochemical anomaly could help to extract reasonable anomalies. In this paper, multiple-point geostatistical simulation and local singularity analysis (LSA) are proposed to identify regional geochemical anomalies and potential mineral resources areas. Taking Cu geochemical data in the Mila Mountain Region, southern Tibet, as an example, several conclusions were obtained: (1) geochemical mapping based on the direct sampling (DS) algorithm of multiple-point geostatistics can avoid the smoothing effect through geochemical pattern simulation; (2) 200 realizations generated by the direct sampling simulation reflect the uncertainty of an unsampled value, and the geochemical anomaly of each realization can be extracted by local singularity analysis, which shows geochemical anomaly uncertainty; (3) the singularity-quantile (S-Q) analysis method was used to determine the separation thresholds of E-type α, and uncertainty analysis was carried out on the copper anomaly to obtain the anomaly probability map, which should be more reasonable than the interpolation-based geochemical map for geochemical anomaly identification. According to the anomaly probability and favorable geological conditions in the study area, several potential mineral resource targets were preliminarily delineated to provide direction for subsequent mineral exploration.

Mapping high-resolution basal topography of West Antarctica from radar data using non-stationary multiple-point geostatistics (MPS-BedMappingV1)

The subglacial bed topography is critical for modeling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to high uncertainty. This is mainly because the bed topography is measured by airborne ice-penetrating radar along flight lines with large gaps up to tens of kilometers. Deterministic interpolation approaches do not reflect such spatial uncertainty. While traditional geostatistical simulation can model such uncertainty, it may be difficult to apply because of the significant non-stationary spatial variation of topography over such large surface area. In this study, we develop a non-stationary multiple-point geostatistical approach to interpolate large areas with irregular geophysical data and apply it to model the spatial uncertainty of entire ASE basal topography. We collect 166 high-resolution topographic training images (TIs) to train the gap-filling of radar data gaps, thereby simulating realistic topography maps. The TIs are extensively sampled from deglaciated regions in the Arctic as well as Antarctica. To address the non-stationarity in topographic modeling, we introduce a Bayesian framework that models the posterior distribution of non-stationary training images to the local modeling domain. Sampling from this distribution then provide candidate training images for local topographic modeling with uncertainty, constrained to radar flight line data. Compared to traditional MPS approaches without considering TI sampling, our approach demonstrates significant improvement in the topographic modeling quality and efficiency of the simulation algorithm. Finally, we simulate multiple realizations of high-resolution ASE topographic maps. We use the multiple realizations to investigate the impact of basal topography uncertainty on subglacial hydrological flow patterns.

SeReMpy: Seismic Reservoir Modeling Python library

Seismic reservoir characterization is a subfield of geophysics that combines seismic and rock physics modeling with mathematical inverse theory to predict the reservoir variables from the measured seismic data. An open-source comprehensive modeling library that includes the main concepts and tools is still missing. We present a Python library named SeReMpy with the state of the art of seismic reservoir modeling for reservoir properties characterization using seismic and rock physics models and Bayesian inverse theory. The most innovative component of the library is the Bayesian seismic and rock physics inversion to predict the spatial distribution of petrophysical and elastic properties from seismic data. The inversion algorithms include Bayesian analytical solutions of the linear-Gaussian inverse problem and Markov chain Monte Carlo (McMC) numerical methods for non-linear problems. The library includes four modules: geostatistics, rock physics, facies, and inversion, as well as several scripts with illustrative examples and applications. We present a detailed description of the scripts that illustrate the use of the functions of module and describe how to apply the codes to practical inversion problems using synthetic and real data. The applications include a rock physics model for the prediction of elastic properties and facies using well log data, a geostatistical simulation of continuous and discrete properties using well logs, a geostatistical interpolation and simulation of two-dimensional maps of temperature, an elastic inversion of partial stacked seismograms with Bayesian linearized AVO inversion, a rock physics inversion of partial stacked seismograms with McMC methods, and a two-dimensional seismic inversion.

Model of Prediction of Gas Emission based on Gas Content Uncertainty in Coal Mine using Geostatistical Simulation and Monte Carlo Method

It is very difficult to predict the emission of coal gas before the extraction, because it depends on various geological, geographical and operational factors. Gas content is a very important parameter for assessing gas emission in the coal seam during and after the extraction. Large amounts of gas released during the mining cause concern about adequate airflow for the ventilation and worker safety. Hence, the performance of the ventilation system is very important in an underground mine. In this paper, the gas content uncertainty in a coal seam is first investigated using the central data of 64 exploratory boreholes. After identifying the important coal seams in terms of gas emission, the variogram modeling for gas content was performed to define the distribution. Consecutive simulations were run for the random evaluation of gas content. Then, a method was proposed to predict gas emission based on the Monte Carlo random simulation method. In order to improve the reliability and precision of gas emission prediction, various factors affecting the gas emission were investigated and the main factors determining the gas emission were identified based on a sensitivity analysis on the mine data. This method produced relative and average errors of 2% and 0.57%, respectively. The results showed that the proposed model is accurate enough to determine the amount of emitted gas and ventilation. In addition, the predicted value was basically consistent with the actual value and the gas emission prediction method based on the uncertainty theory is reliable.

Seismic Lithofacies Distribution Modeling Using the Single Normal Equation Simulation (SNESIM) Algorithm of Multiple-Point Geostatistics in Upper Assam Basin, India

Recently, multiple-point geostatistical simulation gained much attention for its role in spatial reservoir characterization/modeling in geosciences. Accurate lithofacies modeling is a critical step in the characterization of complex geological reservoirs. In this study, multiple-point facies geostatistics based on the SNESIM algorithm integrated with the seismic modeling technique is used as an efficient reservoir modeling approach for lithofacies modeling of the fluvial Tipam formation in the Upper Assam Basin, India. The Tipam formation acts as a potential reservoir rock in the Upper Assam Basin, India. Due to the basin geological complexity and limitation in seismic resolution, many discontinuities in depositional channels in this fluvial depositional environment have been identified using conventional lithofacies mapping. This study combines three techniques to reproduce continuity of the lithofacies for better reservoir modeling. The first is simultaneous prestack inversion for inverting prestack gathers with angle-dependent wavelets into seismic attributes. A cross-plot of P-impedance and VP/VS ratio from well-log data was used to classify the different reservoir lithofacies such as hydrocarbon sand, brine sand, and shale. The second is the Bayesian approach that incorporates probability density functions (PDFs) of non -parametric statistical classification with seismic attributes for converting the seismic attributes into lithofacies volume and the probability volumes of each type lithofacies. The third technique is multiple-point geostatistical simulation (MPS) using the Single Normal equation Simulation (SNESIM) algorithm applied to training images and probability volumes as constraints for a better lithofacies model. These integrated study results proved that MPS could improve reservoir lithofacies characterization.

3D multiple-point geostatistical simulation of joint subsurface redox and geological architectures

Nitrate contamination of subsurface aquifers is an ongoing environmental challenge due to nitrogen (N) leaching from intensive N fertilization and management on agricultural fields. The distribution and fate of nitrate in aquifers are primarily governed by geological, hydrological and geochemical conditions of the subsurface. Therefore, we propose a novel approach to modeling both geology and redox architectures simultaneously in high-resolution 3D (25m×25m×2m) using multiple-point geostatistical (MPS) simulation. Data consist of (1) mainly resistivities of the subsurface mapped with towed transient electromagnetic measurements (tTEM), (2) lithologies from borehole observations, (3) redox conditions from colors reported in borehole observations, and (4) chemistry analyses from water samples. Based on the collected data and supplementary surface geology maps and digital elevation models, the simulation domain was subdivided into geological elements with similar geological traits and depositional histories. The conceptual understandings of the geological and redox architectures of the study system were introduced to the simulation as training images for each geological element. On the basis of these training images and conditioning data, independent realizations were jointly simulated of geology and redox inside each geological element and stitched together into a larger model. The joint simulation of geological and redox architectures, which is one of the strengths of MPS compared to other geostatistical methods, ensures that the two architectures in general show coherent patterns. Despite the inherent subjectivity of interpretations of the training images and geological element boundaries, they enable an easy and intuitive incorporation of qualitative knowledge of geology and geochemistry in quantitative simulations of the subsurface architectures. Altogether, we conclude that our approach effectively simulates the consistent geological and redox architectures of the subsurface that can be used for hydrological modeling with nitrogen (N) transport, which may lead to a better understanding of N fate in the subsurface and to future more targeted regulation of agriculture.

Using digital soil hydraulic maps to simulate water balance at the regional scale (southern Portugal) - impact of spatial resolution and modelling approach

<p>Modelling of soil physical, chemical, and biological processes is critical to improve the understanding of soil functions, the effect of agricultural practices on soil degradation, and appropriate soil management strategies. However, the use of such tools at the regional scale is largely limited by the lack of accurate mapping of soil texture and soil hydraulic properties (SHP). To overcome this limitation, SHP digital maps were obtained using two modelling approaches. One used a national harmonized soil texture database and geostatistical simulation to create soil texture maps which were further used as input data to derive SHP maps using local pedotransfer functions (PTFs). The other approach used SHP maps produced by Tóth et al (2017) using soil texture from the product SoilsGrids (Hengl et al, 2017). The SHP maps from both approaches were produced at two spatial resolutions: 250 m and 1000 m. This study aims to evaluate the usefulness of such SHP maps to simulate soil water dynamics and biomass growth at the regional scale using the MOHID-Land model. This model describes the movement of water in the porous medium based on mass and momentum conservation equations that are computed in a 3D grid domain using a finite volume approach. Crop development is simulated using a modified version of the EPIC model. The SHP maps produced using the two modelling approaches and considering two spatial resolutions (250 and 1000 m) were used as inputs for the hydraulic characteristics of soils. Simulations were compared for an irrigation area (Roxo Irrigation District), located in southern Portugal. Results revealed the differences in the components of the soil water balance, with soil inputs from local data being able to better portray landscape heterogeneity.</p>